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Consider circle [tex]\( T \)[/tex] with radius 24 in. and [tex]\(\theta=\frac{5 \pi}{6}\)[/tex] radians.

What is the length of minor arc [tex]\( SV \)[/tex]?

A. [tex]\(20 \pi\)[/tex] in.
B. [tex]\(28 \pi\)[/tex] in.
C. [tex]\(40 \pi\)[/tex] in.
D. [tex]\(63 \pi\)[/tex] in.

Sagot :

GinnyAnswer
To find the length of the minor arc SV in circle [tex]\( T \)[/tex] with radius 24 inches and central angle [tex]\(\theta = \frac{5\pi}{6}\)[/tex] radians, we use the formula for arc length:

[tex]\[ \text{Arc Length} = \theta \times \text{Radius} \][/tex]

Step-by-step, let's proceed:

1. Identify the given values:
- Radius, [tex]\( r = 24 \)[/tex] inches
- Central angle, [tex]\( \theta = \frac{5\pi}{6} \)[/tex] radians

2. Substitute the values into the formula:

[tex]\[ \text{Arc Length} = \frac{5\pi}{6} \times 24 \][/tex]

3. Multiply the constants:

[tex]\[ \text{Arc Length} = \frac{5\pi}{6} \times 24 = 20\pi \][/tex]

So, the length of the minor arc SV is:

[tex]\[ 20\pi \text{ inches} \][/tex]

This matches one of the given options.

[tex]\[ \boxed{20\pi} \][/tex]
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